# In the given figure, PT is a tangent to the circle with center O. If OT = 6 cm and OP = 10 cm, then the length of tangent PT isA. 8 cmB. 10 cmC. 12 cmD. 16 cm

We have given, PT is a tangent drawn at point T on the circle.

OT TP

[Tangents drawn at a point on circle is perpendicular to the radius through point of contact]

So, In OTP we have,

By Pythagoras Theorem,

[i.e. (Hypotenuse)2 = (Base)2 + (Perpendicular)2]

(OP)2 = (OT)2 + (PT)2

(10)2 = (6)2 + (PT)2

(PT)2 = 100 - 36

(PT)2 = 64

PT = 8 cm

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